MinT - Best Known (120, 120+47, s)-Nets in Base 3

Best Known (120, 120+47, s)-Nets in Base 3

(120, 120+47, 252)-Net over F₃ — Constructive and digital

Digital (120, 167, 252)-net over F₃, using

1 times m-reduction [i] based on digital (120, 168, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 56, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(120, 120+47, 471)-Net over F₃ — Digital

Digital (120, 167, 471)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+47, 13069)-Net in Base 3 — Upper bound on s

There is no (120, 167, 13070)-net in base 3, because

1 times m-reduction [i] would yield (120, 166, 13070)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15 947864 736677 685997 265453 237089 292697 555704 388642 852441 114614 295994 417379 609433 > 3¹⁶⁶ [i]